Satisfiability of ECTL∗ with Local Tree Constraints

Carapelle, Claudia; Feng, Shiguang; Kartzow, Alexander; Lohrey, Markus

doi:10.1007/s00224-016-9724-y

Cited by 4 publications

(2 citation statements)

References 16 publications

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“…However, the way the concrete domain is integrated into the DL in [35] is different from the classical one employed by us and used in all other papers on DLs with concrete domains. In [35], constraints are always placed along a linear path stemming from a single individual, which is rather similar to the use of constraints in temporal logics [36,40]. In contrast, in the classical setting of DLs with concrete domains, one can compare feature values of siblings of an individual.…”

Section: Discussionmentioning

confidence: 99%

Using Model Theory to Find Decidable and Tractable Description Logics with Concrete Domains

Baader

Rydval

2022

J Autom Reasoning

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Concrete domains have been introduced in the area of Description Logic to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. Unfortunately, in the presence of general concept inclusions (GCIs), which are supported by all modern DL systems, adding concrete domains may easily lead to undecidability. To regain decidability of the DL $$\mathcal {ALC}$$ ALC in the presence of GCIs, quite strong restrictions, in sum called $$\omega $$ ω -admissibility, were imposed on the concrete domain. On the one hand, we generalize the notion of $$\omega $$ ω -admissibility from concrete domains with only binary predicates to concrete domains with predicates of arbitrary arity. On the other hand, we relate $$\omega $$ ω -admissibility to well-known notions from model theory. In particular, we show that finitely bounded homogeneous structures yield $$\omega $$ ω -admissible concrete domains. This allows us to show $$\omega $$ ω -admissibility of concrete domains using existing results from model theory. When integrating concrete domains into lightweight DLs of the $$\mathcal {EL}$$ EL family, achieving decidability is not enough. One wants reasoning in the resulting DL to be tractable. This can be achieved by using so-called p-admissible concrete domains and restricting the interaction between the DL and the concrete domain. We investigate p-admissibility from an algebraic point of view. Again, this yields strong algebraic tools for demonstrating p-admissibility. In particular, we obtain an expressive numerical p-admissible concrete domain based on the rational numbers. Although $$\omega $$ ω -admissibility and p-admissibility are orthogonal conditions that are almost exclusive, our algebraic characterizations of these two properties allow us to locate an infinite class of p-admissible concrete domains whose integration into $$\mathcal {ALC}$$ ALC yields decidable DLs.

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Section: Discussionmentioning

confidence: 99%

Using Model Theory to Find Decidable and Tractable Description Logics with Concrete Domains

Baader

Rydval

2022

J Autom Reasoning

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“…Moreover, the string domain pΣ ˚, ă, ", p" w q wPΣ ˚q, in the following denoted by D Σ , is known to be difficult to handle, see e.g. [13,Theorem 1]. This applies also to the concrete domain N (which can be understood as the string domain D Σ with a singleton alphabet), but for this one, the remarkable works [15,27,26] lead to the Exp-Time-completeness of reasoning tasks for the description logic ALCF P pZq.…”

Section: Introductionmentioning

confidence: 99%

First Steps Towards Taming Description Logics with Strings

Demri,

Quaas

2023

Lecture Notes in Computer Science

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We consider the description logic ALCF P pDΣq over the concrete domain DΣ " pΣ ˚, ă, ", p"wq wPΣ ˚q, where ă is the strict prefix order over finite strings in Σ ˚. Using an automata-based approach, we show that the concept satisfiability problem w.r.t. general TBoxes for ALCF P pDΣq is ExpTime-complete for all finite alphabets Σ. As far as we know, this is the first complexity result for an expressive description logic with a nontrivial concrete domain on strings.‹ The second author is supported by the Deutsche Forschungsgemeinschaft (DFG), project 504343613.

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Description Logics with Concrete Domains and General Concept Inclusions Revisited

Baader

Rydval

2020

Automated Reasoning

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Satisfiability of ECTL∗ with Local Tree Constraints

Cited by 4 publications

References 16 publications

Using Model Theory to Find Decidable and Tractable Description Logics with Concrete Domains

Using Model Theory to Find Decidable and Tractable Description Logics with Concrete Domains

First Steps Towards Taming Description Logics with Strings

Description Logics with Concrete Domains and General Concept Inclusions Revisited

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